I installed a copy of the current master branch from github.
Logged into admin panel and browsed around. Played with the site a little. Everything seemed great except I wanted to turn on seo.
I did everything needed and the last step was turning it on in the settings. Eventually I found the settings and I changed some of the others, like store title.
After saving, I was redirected out of the admin panel back to the login. I figured my login session had expired (as I had left this tab open for awhile). So, I tried to re-login, but now whenever I try to login to the admin panel I am redirected back a url like below...

Never use the version on github. It's the one currently being worked on, so it almost always has bugs or broken features in it. Always use the last official version released, which you can to by going to Resources > Download up in the header menu bar.

The current version is 3.0.2.0, but it's been almost a year since that's been updated. It also still has a few bugs, so you should make sure to check the 3.0.2.0 bug topic (or the github issues log) to find the fixes for those. If you can wait, I'd highly recommend waiting until 3.1.0.0 is officially released, though there's no telling when that will be.

Hmm. Granted, I didn't do a super detailed look-through, but it didn't seem as if anything that could cause this issue has had an updates in a long time. Which makes me think this has nothing to do with on-going development. Does this mean nobody will help with a copy from git?

On a side note, as a developer, I feel like the master branch should be a somewhat stable version while development happens in other branches. If this is not the case, the website should probably not suggest it as a form of downloading the cart system (look at the download page and it's suggested as an equivalent but alternate means of download).

Well, better accept OC, as it comes, we all have our little misses and faults, but
zero influence, when it comes to strategic or technical ways of doing OC things.
It's just the way, how this Project works, OC is no 'common' goal, but simply
Business. And many Newbies are just not aware of this, at first at least ...
Good Luck !
Ernie

If this is not the case, the website should probably not suggest it as a form of downloading the cart system (look at the download page and it's suggested as an equivalent but alternate means of download).

On a side note, as a developer, I feel like the master branch should be a somewhat stable version while development happens in other branches.

Yeah, we all do. Daniel is the one that controls that, though, so we all have to work with the official versions, and bugfix them as necessary when a bugfixed version isn't released. It's the unfortunate reality of how OpenCart works currently, but it's up to you if you want to use the github version or the official version, and work on fixing bugs from there. (In my experience, the github version has too much flux, and it gets to be too complicated to constantly be fixing issues on changing code. That's why I usually suggest the official version, which at least is a known quantity in terms of bugs present.)